U.S. Pat. No. 4,391,774, granted July 5,1983, which corresponds to French Patent Application No. 80.14302 filed on June 27, 1980, describes an apparatus for analyzing samples of the raw mix being fed to a cement kiln. This apparatus is designed for automatically producing vitrified samples called "pearls" which will subsequently be analyzed by an X-ray spectrometer. This apparatus comprises a swivelling arm carrying tongs for handling a crucible, in combination with a weighing system and a furnace. Using this apparatus, it is possible to obtain automatically and rapidly an analysis of the components of the raw mix being fed to a cement kiln. However, after the cement has left the kiln and after the clinker has been crushed, there remains the need to add to this clinker additives such as gypsum and limestone filler. There is also the need to monitor the regularity of the grain size distribution of the finished cement.